1. Write an expression for each of the following:

a. the sum of 6 and z

b. the difference between 20 and x

c. 8 less than the quotient of x divided by 6

d. x increased by 5 divided by 4

2. Simplify:

a. 7x + 3x

b. 6s - 3s + 4s

c. 4T - 6T

d. 4xy + 3xy + x

e. (6x)2

f. 6x
xx2x

3. Add or subtract the following terms:

a. (10x) + (22x) =

b. (-6x) - (-6x) =

c. (-13t) + (14x) - (+13t) =

d. (-4t) + (+4t) - (-3t) =

4. Multiply the following signed numbers:

a. (-42x)(+2x) =

b. (+8x)(-4x)(-3x) =

c. (+7)(-4)(-4) =

d. (+10)(-2)(-2)(+4) =

5. Divide the following signed numbers:

a. \LARGE \frac{-4}{-2}

b. \LARGE \frac{-2}{-1}

c. \LARGE \frac{-24}{-48}

6. Solve the following equations:

a. x + 6 = 28

b. y - 5 = 30

c. s + 2s = 36

d. t - t + 4t = 16

e. 5a = 15

f. 8x - x = 21

7. Add or subtract the following polynomials:

a. 2x2 + 3y3 - 4x2 =

b. y3 + 2y3 - 8 + 2 =

c. 10 - 3x - 4x + 2x - 12 =

d. -6t + 4t2 - 6 + 7t - 4t2 =

8. Multiply the following:

a. (x3)(x2) =

b. (x7)(x10) =

c. (2s4)(-6s5) =

d. (-30x)(3x) =

9. Divide the following:

a. x4 / x3

b. s3 / s5

c. z12 / z10

10. Remove the parentheses by multiplication:

a. 6(3a-4) =

b. x(2x + 10) =

c. 9(9x-9) =

d. 2x(2x-x) =

11. Solve the following equations:

a. 2(x-4) = 10

b. 3x(4x + 3x) = 21

c. 3(4-2x) = 24

d. 10x(2 + 13) = 300

12. Multiply the following binomials:

a. (x + 3)(x - 4)

b. (s - 2)(2s - 12)

c. (6s - 12)(2s + 4)

d. (2x - 4)(2x - 4)

13. Solve the following inequalities:

a. 3x - 3 > 9

b. 24x + 4 < 52

c. -2x - 2 < 8

d. 10x - 100 > 0

14. Factor the following:

a. x2 - 25

b. y2 - 64

c. x2 - 14x + 13

d. s2 + 7s + 10

e. q2 - 7q + 12

f. r2 + 13r + 12

g. x2 - x - 20

h. y2 + 5y + 6

i. b2 + b - 12

j. k2-5k + 6